scholarly journals Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Muhammad Jamil ◽  
Asmat Ara
Keyword(s):  
Approximate Solution ◽  
Nonlinear Oscillator ◽  
High Accuracy ◽  
Force Term ◽  
Hamiltonian Approach ◽  
New Approach ◽  
Suggested Technique ◽  
Multiple Parameter ◽  
Approximate Frequency ◽  
Relationship Of

We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique.

scholarly journals Dynamic Analysis of Rotating Pendulum by Hamiltonian Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Najeeb Alam Khan ◽  
Nadeem Alam Khan ◽  
Fatima Riaz
Keyword(s):  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Natural Frequency ◽  
Governing Equation ◽  
Conservative System ◽  
Hamiltonian Approach ◽  
Series Approximation ◽  
Suggested Technique ◽  
Approximate Frequency ◽  
Relationship Of

A conservative system always admits Hamiltonian invariant, which is kept unchanged during oscillation. This property is used to obtain the approximate frequency-amplitude relationship of the governing equation with sinusoidal nonlinearity. Here, we applied Hamiltonian approach to obtain natural frequency of the nonlinear rotating pendulum. The problem has been solved without series approximation and other restrictive assumptions. Numerical simulations are then conducted to prove the efficiency of the suggested technique.

Frequency–Amplitude Relationship of Coupled Anharmonic Oscillators

2011 ◽  
Vol 105-107 ◽  
pp. 271-274
Author(s):  
Zheng Biao Li ◽  
Wei Hong Zhu
Keyword(s):  
Approximate Solution ◽  
Nonlinear Oscillator ◽  
Nonlinear Problems ◽  
Solution Procedure ◽  
Parameter Method ◽  
Anharmonic Oscillators ◽  
First Order ◽  
Linear And Nonlinear ◽  
Relationship Of

The frequency–amplitude relationship of coupled anharmonic oscillators is an important problem. Many powerful methods for solving this problem have been proposed. He’s parameter-expanding method is an important one. It holds the advantages of modified Lindstedt–Poincare parameter method and bookkeeping parameter method. The first iteration is enough. It is very effective and convenient and quite accurate to both linear and nonlinear problems. In this paper, He’s parameter-expanding method is applied to coupled anharmonic oscillators. The frequency-amplitude relationship and the first-order approximate solution of the oscillators are obtained respectively. The solution procedure shows that the method is very powerful and convenient to nonlinear oscillator. This method has great potential and can be applied to other types of nonlinear oscillator problems.

scholarly journals Higher-Order Approximate Periodic Solutions of a Nonlinear Oscillator with Discontinuity by Variational Approach

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
M. Orhan Kaya ◽  
S. Altay Demirbağ ◽  
F. Özen Zengin
Keyword(s):  
Approximate Solution ◽  
Periodic Solutions ◽  
Relative Error ◽  
Variational Approach ◽  
Nonlinear Oscillator ◽  
Higher Order ◽  
Second Order ◽  
Elastic Force ◽  
Force Term ◽  
The Third

He's variational approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). Three levels of approximation have been used. We obtained 1.6% relative error for the first approximate period, 0.3% relative error for the second-order approximate period. The third approximate solution has the accuracy as high as 0.1%.

Colonialism and the Highland Clearances

2017 ◽  
Vol 8 (1) ◽  
pp. 22-48 ◽  
Author(s):  
Iain Mackinnon
Keyword(s):  
Industrial Development ◽  
Comparative Approach ◽  
Indigenous Research ◽  
Internal Colonialism ◽  
New Approach ◽  
A Site ◽  
Relationship Of ◽  
The Relationship ◽  
Imperial State ◽  
Late Modern

This article employs a new approach to studying internal colonialism in northern Scotland during the 18th and 19th centuries. A common approach to examining internal colonial situations within modern state territories is to compare characteristics of the internal colonial situation with attested attributes of external colonial relations. Although this article does not reject the comparative approach, it seeks to avoid criticisms that this approach can be misleading by demonstrating that promoters and managers of projects involving land use change, territorial dispossession and industrial development in the late modern Gàidhealtachd consistently conceived of their work as projects of colonization. It further argues that the new social, cultural and political structures these projects imposed on the area's indigenous population correspond to those found in other colonial situations, and that racist and racialist attitudes towards Gaels of the time are typical of those in colonial situations during the period. The article concludes that the late modern Gàidhealtachd has been a site of internal colonization where the relationship of domination between colonizer and colonized is complex, longstanding and occurring within the imperial state. In doing so it demonstrates that the history and present of the Gaels of Scotland belongs within the ambit of an emerging indigenous research paradigm.

scholarly journals A New Approach for Approximate Solution of ADE: Physical-Based Modeling of Carriers in Doping Region

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 458
Author(s):  
Leobardo Hernandez-Gonzalez ◽  
Jazmin Ramirez-Hernandez ◽  
Oswaldo Ulises Juarez-Sandoval ◽  
Miguel Angel Olivares-Robles ◽  
Ramon Blanco Sanchez ◽  
...  
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Order Differential Equation ◽  
Electric Circuit ◽  
New Approach ◽  
In Doping ◽  
Electric Behavior ◽  
Spatio Temporal ◽  
Physical Phenomena

The electric behavior in semiconductor devices is the result of the electric carriers’ injection and evacuation in the low doping region, N-. The carrier’s dynamic is determined by the ambipolar diffusion equation (ADE), which involves the main physical phenomena in the low doping region. The ADE does not have a direct analytic solution since it is a spatio-temporal second-order differential equation. The numerical solution is the most used, but is inadequate to be integrated into commercial electric circuit simulators. In this paper, an empiric approximation is proposed as the solution of the ADE. The proposed solution was validated using the final equations that were implemented in a simulator; the results were compared with the experimental results in each phase, obtaining a similarity in the current waveforms. Finally, an advantage of the proposed methodology is that the final expressions obtained can be easily implemented in commercial simulators.

A New Numerical Method for Solving Nonlinear Fractional Fokker–Planck Differential Equations

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
BeiBei Guo ◽  
Wei Jiang ◽  
ChiPing Zhang
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Reproducing Kernel ◽  
Numerical Solutions ◽  
Simple Algorithm ◽  
High Accuracy ◽  
Computational Work ◽  
Reproducing Kernel Theory ◽  
Transport Problems ◽  
Fokker Planck

The nonlinear fractional-order Fokker–Planck differential equations have been used in many physical transport problems which take place under the influence of an external force filed. Therefore, high-accuracy numerical solutions are always needed. In this article, reproducing kernel theory is used to solve a class of nonlinear fractional Fokker–Planck differential equations. The main characteristic of this approach is that it induces a simple algorithm to get the approximate solution of the equation. At the same time, an effective method for obtaining the approximate solution is established. In addition, some numerical examples are given to demonstrate that our method has lesser computational work and higher precision.

Antecedents of relationship conflict in top management teams

2014 ◽  
Vol 25 (2) ◽  
pp. 124-147 ◽  
Author(s):  
Carmen Camelo-Ordaz ◽  
Joaquin García-Cruz ◽  
Elena Sousa-Ginel
Keyword(s):  
Top Management Teams ◽  
Management Teams ◽  
Relationship Conflict ◽  
Top Management ◽  
New Approach ◽  
Content Type ◽  
Behavioral Integration ◽  
Measurement Analysis ◽  
And Behavior ◽  
Relationship Of

Purpose – The aim of this paper is to analyze the influence of two categories of conflict antecedents – input and behavior antecedents – on the level of relationship conflict (RC) in top management teams (TMTs). The authors apply a process view to conflict, and consider that the effect of the input antecedents on RC may be mediated by a behavioral antecedent: behavioral integration. Design/methodology/approach – Using a survey instrument, multi-informant data were collected from 64 TMTs. An aggregation and measurement analysis was performed. To test the hypotheses of mediation, bootstrapping procedures were used. Findings – The results show that the effects of team tenure, intragroup trust and value consensus on relationship conflict are mediated by behavioral integration. However, TMT size does not affect relationship conflict – either directly or indirectly – through behavioral integration. Research limitations/implications – It is concluded that encouraging intragroup trust and value consensus among TMT members facilitates the integrated behavior of the team. This behavioral integration may allow conflict to be constructive. Therefore, firms should make an effort to encourage this psychological context. Originality/value – Previous research about the antecedents of RC in the field of TMTs is inconclusive. Additionally, a new approach to conflict antecedents is considered, to establish a direct and independent relationship between different categories of antecedents and TMT conflict. A relationship of interdependence is considered between different types of antecedents and their effects on RC.

Understanding Statistics Cognition

2017 ◽  
pp. 10-56
Keyword(s):  
Cognitive Processes ◽  
New Approach ◽  
Relationship Of ◽  
The Relationship

This chapter focuses on understanding the use of and relationship among the features of statistics cognition: literacy, reasoning, and thinking. We argue that research on statistics cognition is fragmented, which is problematic for understanding how these constructs can be unified to support education. We then review methods of quantifying cognitions, involving studies which have attempted to categorize and parse cognitive processes. This information is then used to synthesize a new approach to understanding statistics cognition, proposing a model which makes specific predictions about the relationship of these features. The model and definitions of cognitions presented in this chapter are used as a basis of discussion cognition throughout the remainder of the book.

scholarly journals A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Alvaro H. Salas S ◽  
Jairo E. Castillo H ◽  
Darin J. Mosquera P
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Initial Conditions ◽  
Negative Ions ◽  
Nonlinear Problems ◽  
New Approach ◽  
Weierstrass Elliptic Function ◽  
Electronegative Plasma ◽  
The Given

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

scholarly journals High-accuracy equation of equinoxes and VLBI astrometric Modelling

1991 ◽  
Vol 131 ◽  
pp. 342-345
Author(s):  
A.M. Gontier ◽  
N. Capitaine
Keyword(s):  
High Accuracy ◽  
Classical Representation ◽  
New Approach ◽  
The Earth ◽  
Angle Of Rotation

AbstractIn the course of implementing the use of nonrotating origin (Guinot 1979) in astrometric VLBI, for the transformation between celestial and terrestrial frames, we have compared the new approach with the classical one. We have shown that a difference exists between the two procedures at a few milliarcsecond level; this difference is due to the terms generally neglected when considering the equation of equinoxes in the classical representation of the Earth angle of rotation.

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